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Force/Pressure - Easy Question I think

  1. Jun 3, 2004 #1
    We were doing simple [tex]P=\rho g h[/tex] problems in class and then all of a sudden I ran into these two when I was doing my homework. We never went over this in class and I have no idea what to do.

    1. A whale tank at the zoo is 15 feet deep and filled with sea water. A 6 foot tall by 20 foot wide observation window is on one wall. If the bottom of the window is 3ft above the floor of the tank, what total force does the water exert on the window?

    2. Find the force on one square foot side panel that is on the side of a concrete form at the bottom. The form is filled with liquid concrete of specific gravity 2.62. The form is 5/6 ft thick x 8 ft wide x 8 ft tall.

    I just need a little help to put me in the right direction. Any help would be much appreciated.
  2. jcsd
  3. Jun 3, 2004 #2
    I believe this is the relationship you need:

    [tex]F=\rho g h_c A[/tex]

    F is the total force of the fluid acting on the submerged area, [tex]h_c[/tex] is the vertical depth of the area's centroid, and A is the area you are considering. This says that the hydrostatic force acting on a plane area is equal to the pressure at the area's centroid times the area itself.

    In the case of the first problem, the area is simply 6*20 ft^2, and the depth of the centroid should be 9 ft (window top is 6 ft from water's surface, window centroid is at the middle of the window).

    You should be able to apply the same principle to the second problem.

    The above is true for a submerged plane area regardless of its shape or orientation (horizontal, vertical, inclined, whatever). However, while the hydrostatic force is equal to the pressure at the centroid times the area, the force doesn't necessarily act through the centroid. It's more complicated to find exactly where the force acts (the so-called "center of pressure").
    Last edited: Jun 3, 2004
  4. Jun 3, 2004 #3
    Great, answers came out like they should. Thanks a lot.
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